Two-stage estimation and simultaneous confidence band in partially nonlinear additive model

Rui Li () and Yuanyuan Zhang
Additional contact information
Rui Li: Shanghai University of International Business and Economics
Yuanyuan Zhang: Shanghai University of International Business and Economics

Metrika: International Journal for Theoretical and Applied Statistics, 2021, vol. 84, issue 8, No 2, 1109-1140

Abstract: Abstract In this paper, we focus on the estimation and inference in partially nonlinear additive model on which few research was conducted to our best knowledge. By integrating spline approximation and local smoothing, we propose a two-stage estimating approach in which the profile nonlinear least square method was used to estimate parameters and additive functions. Under some regular conditions, we establish the asymptotic normality of parametric estimators and achieve an optimal nonparametric convergence rate of the fitted functions. Furthermore, the spline-backfitted local linear estimator is proposed for the additive functions and the corresponding asymptotic distribution is also established. To make inference on the nonparametric functions from the whole, we construct the theoretical simultaneous confidence bands, and further propose an empirical bootstrap-based confidence band for the heavy computing burden in implement. Finally, both Monte Carlo simulation and real data analysis show the good performance of our proposed methods.

Keywords: B-spline; Local linear; Simultaneous confidence band; Two-stage estimation; 62G05; 62G20; 62E20 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00184-021-00808-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:84:y:2021:i:8:d:10.1007_s00184-021-00808-3

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/184/PS2

DOI: 10.1007/s00184-021-00808-3

Access Statistics for this article

Metrika: International Journal for Theoretical and Applied Statistics is currently edited by U. Kamps and Norbert Henze

More articles in Metrika: International Journal for Theoretical and Applied Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().